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Possible halo structure of $^{62,72}$Ca by forbidden-state-free locally peaked Gaussians

In order to efficiently describe nucleon orbits around a heavy core nucleus, we propose locally peaked Gaussians orthogonalized to the occupied bound states in the core. We show the advantage of those functions in both numerical stability and fast convergence by taking examples of touchstone calcium isotopes $^{62,72}$Ca in $^{60,70}{\rm Ca}+n+n$ three-body models. Both weakly bound configurations and continuum coupling effect are taken into account. We evaluate the neutron radii and the occupation probabilities of two-neutron configurations not only for the ground state but also for some particle-bound excited states by varying the strength of the core-neutron interaction. The emergence of the halo structure in the ground state depends on the energy difference between $2s_{1/2}$ and $0g_{9/2}$ orbits. Two-neutron [consisting of $(s_{1/2})^2$ configuration] and one-neutron [consisting of $(g_{9/2}s_{1/2})$ configuration] halo structure of $^{62}$Ca can coexist in narrow energy spacing provided that both of $2s_{1/2}$ and $0g_{9/2}$ orbits are almost degenerate and barely bound. The ground-state structure of $^{72}$Ca is likely to be a two-neutron halo, although its emergence depends on the position of the $2s_{1/2}$ level.